Extensive Form

Definition

Extensive form is a way of representing games that shows the sequential nature of decisions made by players, typically using a tree diagram. It highlights the order of moves and the choices available at each decision point, making it easier to analyze dynamic interactions among players. This representation is especially useful for understanding complex strategies and outcomes that depend on the timing of decisions and players' responses.

5 Must Know Facts For Your Next Test

1. Extensive form allows players to see the entire structure of a game, including all possible paths and outcomes, which can help in strategic planning.
2. The representation includes nodes for decision points, branches for possible actions, and terminal nodes for final outcomes, showcasing the game's evolution.
3. Extensive form is particularly useful in games involving sequential moves, where earlier decisions influence later choices.
4. In extensive form games, players can use backward induction to determine optimal strategies by analyzing the last moves first and working backward.
5. Converting from extensive to normal form involves summarizing the strategic options into a payoff matrix, which can simplify the analysis but may lose some sequential insights.

Review Questions

• How does extensive form representation aid in understanding complex games with sequential moves?
  • Extensive form representation aids in understanding complex games by visually outlining the order of decisions and available options at each stage. It allows players to track how earlier choices influence later ones, making it clearer how strategies can evolve over time. This sequential aspect is critical for analyzing dynamic interactions and anticipating opponents' responses based on past moves.
• Discuss the advantages of using extensive form over normal form when analyzing strategic interactions among players.
  • Using extensive form provides several advantages over normal form. It offers a clear depiction of the timing of decisions and the sequence of actions that can significantly affect outcomes. Players can better understand potential strategies by visualizing the entire game's structure, which is particularly important in scenarios where timing matters. Additionally, extensive form facilitates techniques like backward induction, allowing for more thorough analysis of optimal strategies.
• Evaluate how extensive form can impact the concept of subgame perfect equilibrium in strategic decision-making.
  • Extensive form has a significant impact on subgame perfect equilibrium by providing a framework to evaluate players' strategies at every possible decision point within the game. This concept ensures that players' strategies are optimal not just overall but also in every subgame derived from any point in the game tree. The representation enables players to anticipate reactions and plan accordingly, making it easier to identify equilibria that hold true even in more complex scenarios with multiple layers of decision-making.

Related terms

Normal Form:

A representation of a game that summarizes players' strategies and payoffs in a matrix format, showing simultaneous moves rather than sequential decisions.

Game Tree:

A graphical representation of a game in extensive form, illustrating the possible moves, choices, and outcomes as branches in a tree structure.

Subgame Perfect Equilibrium:

A refinement of Nash equilibrium applicable in extensive form games, where players' strategies are optimal not only for the entire game but also for every subgame.